Activities for Students: What Did One Angle Say to the Other Angles?

Robert Oppenheimer (1904–67), the famous theoretical physicist known as the father of the atomic bomb, was once asked how he became such a great scientist. He replied that early on he had teachers who afforded him, as he put it, the joy of discovery . It truly is a joy to discover something for yourself, even if it were previously discovered by someone else. Discovery learning should be a significant part of the mathematics curriculum. Activities that lead students to discover some interesting and perhaps unexpected results are fun for both students and teachers. This article presents an inductive angle-sequence activity that uses paper folding to arrive at a surprising conjecture. Two versions of a second activity leading to deductive verification of the conjecture are also provided. Although these activities are suitable for individual effort, I find that having students work in small groups of three or four students is more enjoyable for them and thus have formatted the activities for group effort.